Research article

A transient biological fouling model for constant flux microfiltration


  • Received: 24 August 2022 Revised: 03 October 2022 Accepted: 10 October 2022 Published: 27 October 2022
  • Microfiltration is a widely used engineering technology for fresh water production and water treatment. The major concern in many applications is the formation of a biological fouling layer leading to increased hydraulic resistance and flux decline during membrane operations. The growth of bacteria constituting such a biological layer implicates the formation of a multispecies biofilm and the consequent increase of operational costs for reactor management and cleaning procedures. To predict the biofouling evolution, a mono-dimensional continuous free boundary model describing biofilm dynamics and EPS production in different operational phases of microfiltration systems has been well studied. The biofouling growth is governed by a system of hyperbolic PDEs. Substrate dynamics are modeled through parabolic equations accounting for diffusive and advective fluxes generated during the filtration process. The free boundary evolution depends on both microbial growth and detachment processes. What is not addressed is the interplay between biofilm dynamics, filtration, and water recovery. In this study, filtration and biofilm growth modeling principles have been coupled for the definition of an original mathematical model able to reproduce biofouling evolution in membrane systems. The model has been solved numerically to simulate biologically relevant conditions, and to investigate the hydraulic behavior of the membrane. It has been calibrated and validated using lab-scale data. Numerical results accurately predicted the pressure drop occurring in the microfiltration system. A calibrated model can give information for optimization protocols as well as fouling prevention strategies.

    Citation: Vincenzo Luongo, Maria Rosaria Mattei, Luigi Frunzo, Berardino D'Acunto, Kunal Gupta, Shankararaman Chellam, Nick Cogan. A transient biological fouling model for constant flux microfiltration[J]. Mathematical Biosciences and Engineering, 2023, 20(1): 1274-1296. doi: 10.3934/mbe.2023058

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  • Microfiltration is a widely used engineering technology for fresh water production and water treatment. The major concern in many applications is the formation of a biological fouling layer leading to increased hydraulic resistance and flux decline during membrane operations. The growth of bacteria constituting such a biological layer implicates the formation of a multispecies biofilm and the consequent increase of operational costs for reactor management and cleaning procedures. To predict the biofouling evolution, a mono-dimensional continuous free boundary model describing biofilm dynamics and EPS production in different operational phases of microfiltration systems has been well studied. The biofouling growth is governed by a system of hyperbolic PDEs. Substrate dynamics are modeled through parabolic equations accounting for diffusive and advective fluxes generated during the filtration process. The free boundary evolution depends on both microbial growth and detachment processes. What is not addressed is the interplay between biofilm dynamics, filtration, and water recovery. In this study, filtration and biofilm growth modeling principles have been coupled for the definition of an original mathematical model able to reproduce biofouling evolution in membrane systems. The model has been solved numerically to simulate biologically relevant conditions, and to investigate the hydraulic behavior of the membrane. It has been calibrated and validated using lab-scale data. Numerical results accurately predicted the pressure drop occurring in the microfiltration system. A calibrated model can give information for optimization protocols as well as fouling prevention strategies.



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    [1] R. V. Linares, A. Wexler, S. S. Bucs, C. Dreszer, A. Zwijnenburg, H. C. Flemming, et al., Compaction and relaxation of biofilms, Desalin. Water Treat., 57 (2016), 12902–12914. https://doi.org/10.1080/19443994.2015.1057036 doi: 10.1080/19443994.2015.1057036
    [2] K. Martin, D. Bolster, N. Derlon, E. Morgenroth, R. Nerenberg, Effect of fouling layer spatial distribution on permeate flux: a theoretical and experimental study, J. Membr. Sci., 471 (2014), 130–137. https://doi.org/10.1016/j.memsci.2014.07.045 doi: 10.1016/j.memsci.2014.07.045
    [3] A. Venezuela, J. Pérez-Guerrero, S. Fontes, Hybrid modeling of convective laminar flow in a permeable tube associated with the cross-flow process, Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 795–810. https://doi.org/10.1016/j.cnsns.2007.11.009 doi: 10.1016/j.cnsns.2007.11.009
    [4] S. F. Anis, R. Hashaikeh, N. Hilal, Microfiltration membrane processes: a review of research trends over the past decade, J. Water Process Eng., 32 (2019), 100941. https://doi.org/10.1016/j.jwpe.2019.100941 doi: 10.1016/j.jwpe.2019.100941
    [5] I. Ivanovic, T. Leiknes, The biofilm membrane bioreactor (bf-mbr)—a review, Desalin. Water Treat., 37 (2012), 288–295. https://doi.org/10.1080/19443994.2012.661283 doi: 10.1080/19443994.2012.661283
    [6] B. D'Acunto, L. Frunzo, V. Luongo, M. R. Mattei, Invasion moving boundary problem for a biofilm reactor model, Eur. J. Appl. Math., 29 (2018), 1079–1109. https://doi.org/10.1017/S0956792518000165 doi: 10.1017/S0956792518000165
    [7] B. D'Acunto, L. Frunzo, V. Luongo, M. R. Mattei, Modeling heavy metal sorption and interaction in a multispecies biofilm, Mathematics, 7 (2019), 781. https://doi.org/10.3390/math7090781 doi: 10.3390/math7090781
    [8] A. Trucchia, M. Mattei, V. Luongo, L. Frunzo, M. Rochoux, Surrogate-based uncertainty and sensitivity analysis for bacterial invasion in multi-species biofilm modeling, Commun. Nonlinear Sci. Numer. Simul., 73 (2019), 403–424. https://doi.org/10.1016/j.cnsns.2019.02.024 doi: 10.1016/j.cnsns.2019.02.024
    [9] C. Dreszer, J. S. Vrouwenvelder, A. H. Paulitsch-Fuchs, A. Zwijnenburg, J. C. Kruithof, H. C. Flemming, Hydraulic resistance of biofilms, J. Membr. Sci., 429 (2013), 436–447. https://doi.org/10.1016/j.memsci.2012.11.030 doi: 10.1016/j.memsci.2012.11.030
    [10] S. Kang, W. Lee, S. Chae, H. Shin, Positive roles of biofilm during the operation of membrane bioreactor for water reuse, Desalination, 202 (2007), 129–134. https://doi.org/10.1016/j.desal.2005.12.048 doi: 10.1016/j.desal.2005.12.048
    [11] S. Kerdi, A. Qamar, A. Alpatova, N. Ghaffour, An in-situ technique for the direct structural characterization of biofouling in membrane filtration, J. Membr. Sci., 583 (2019), 81–92. https://doi.org/10.1016/j.memsci.2019.04.051 doi: 10.1016/j.memsci.2019.04.051
    [12] W. Bowen, J. Calvo, A. Hernandez, Steps of membrane blocking in flux decline during protein microfiltration, J. Membr. Sci., 101 (1995), 153–165. https://doi.org/https://doi.org/10.1016/0376-7388(94)00295-A doi: 10.1016/0376-7388(94)00295-A
    [13] S. Chellam, W. Xu, Blocking laws analysis of dead-end constant flux microfiltration of compressible cakes, J. Colloid Interface Sci., 301 (2006), 248–257. https://doi.org/10.1016/j.jcis.2006.04.064 doi: 10.1016/j.jcis.2006.04.064
    [14] N. Cogan, S. Chellam, Incorporating pore blocking, cake filtration, and eps production in a model for constant pressure bacterial fouling during dead-end microfiltration, J. Membr. Sci., 345 (2009), 81–89. https://doi.org/10.1016/j.memsci.2009.08.027 doi: 10.1016/j.memsci.2009.08.027
    [15] M. Imran, H. L. Smith, A model of optimal dosing of antibiotic treatment in biofilm, Math. Biosci. Eng., 11 (2014), 547. https://doi.org/10.3934/mbe.2014.11.547 doi: 10.3934/mbe.2014.11.547
    [16] C. Laspidou, L. Spyrou, N. Aravas, B. Rittmann, Material modeling of biofilm mechanical properties, Math. Biosci., 251 (2014), 11–15. https://doi.org/10.1016/j.mbs.2014.02.007 doi: 10.1016/j.mbs.2014.02.007
    [17] M. Mattei, L. Frunzo, B. D'Acunto, Y. Pechaud, F. Pirozzi, G. Esposito, Continuum and discrete approach in modeling biofilm development and structure: a review, J. Math. Biol., 76 (2018), 945–1003. https://doi.org/10.1007/s00285-017-1165-y doi: 10.1007/s00285-017-1165-y
    [18] A. Tenore, M. Mattei, L. Frunzo, Modelling the ecology of phototrophic-heterotrophic biofilms, Commun. Nonlinear Sci. Numer. Simul., 94 (2021), 105577. https://doi.org/10.1016/j.cnsns.2020.105577 doi: 10.1016/j.cnsns.2020.105577
    [19] A. Tenore, F. Russo, M. Mattei, B. D'Acunto, G. Collins, L. Frunzo, Multiscale modelling of de novo anaerobic granulation, Bull. Math. Biol., 83 (2021), 1–50. https://doi.org/10.1007/s11538-021-00951-y doi: 10.1007/s11538-021-00951-y
    [20] M. Jafari, N. Derlon, P. Desmond, M. C. van Loosdrecht, E. Morgenroth, C. Picioreanu, Biofilm compressibility in ultrafiltration: a relation between biofilm morphology, mechanics and hydraulic resistance, Water Res., 157 (2019), 335–345. https://doi.org/10.1016/j.watres.2019.03.073 doi: 10.1016/j.watres.2019.03.073
    [21] H. Vrouwenvelder, C. Dreszer, R. V. Linares, J. Kruithof, C. Mayer, H. Flemming, Why and how biofilms cause biofouling–the "hair-in-sink"-effect, in The Perfect Slime: Microbial Extracellular Polymeric Substances (EPS), (2016), 193–206.
    [22] G. Tierra, J. P. Pavissich, R. Nerenberg, Z. Xu, M. S. Alber, Multicomponent model of deformation and detachment of a biofilm under fluid flow, J. R. Soc. Interface, 12 (2015), 20150045. https://doi.org/10.1098/rsif.2015.0045 doi: 10.1098/rsif.2015.0045
    [23] M. Li, K. Matouš, R. Nerenberg, Predicting biofilm deformation with a viscoelastic phase-field model: modeling and experimental studies, Biotechnol. Bioeng., 117 (2020), 3486–3498. https://doi.org/10.1002/bit.27491 doi: 10.1002/bit.27491
    [24] M. Rahimi, S. Madaeni, M. Abolhasani, A. A. Alsairafi, Cfd and experimental studies of fouling of a microfiltration membrane, Chem. Eng. Process. Process Intensif., 48 (2009), 1405–1413. https://doi.org/10.1016/j.cep.2009.07.008 doi: 10.1016/j.cep.2009.07.008
    [25] A. Tenore, J. Vieira, L. Frunzo, V. Luongo, M. Fabbricino, Calibration and validation of an activated sludge model for membrane bioreactor wastewater treatment plants, Environ. Technol., 41 (2020), 1923–1936. https://doi.org/10.1080/09593330.2018.1551940 doi: 10.1080/09593330.2018.1551940
    [26] M. Zare, F. Z. Ashtiani, A. Fouladitajar, Cfd modeling and simulation of concentration polarization in microfiltration of oil–water emulsions; application of an eulerian multiphase model, Desalination, 324 (2013), 37–47. https://doi.org/10.1016/j.desal.2013.05.022 doi: 10.1016/j.desal.2013.05.022
    [27] C. Picioreanu, J. Vrouwenvelder, M. Van Loosdrecht, Three-dimensional modeling of biofouling and fluid dynamics in feed spacer channels of membrane devices, J. Membr. Sci., 345 (2009), 340–354. https://doi.org/10.1016/j.memsci.2009.09.024 doi: 10.1016/j.memsci.2009.09.024
    [28] J. Shin, K. Kim, J. Kim, S. Lee, Development of a numerical model for cake layer formation on a membrane, Desalination, 309 (2013), 213–221. https://doi.org/10.1016/j.desal.2012.10.018 doi: 10.1016/j.desal.2012.10.018
    [29] S. Chellam, N. Cogan, Colloidal and bacterial fouling during constant flux microfiltration: comparison of classical blocking laws with a unified model combining pore blocking and eps secretion, J. Membr. Sci., 382 (2011), 148–157. https://doi.org/10.1016/j.memsci.2011.08.001 doi: 10.1016/j.memsci.2011.08.001
    [30] N. Cogan, J. Li, A. R. Badireddy, S. Chellam, Optimal backwashing in dead-end bacterial microfiltration with irreversible attachment mediated by extracellular polymeric substances production, J. Membr. Sci., 520 (2016), 337–344. https://doi.org/10.1016/j.memsci.2016.08.001 doi: 10.1016/j.memsci.2016.08.001
    [31] B. D'Acunto, L. Frunzo, V. Luongo, M. Mattei, A. Tenore, Free boundary problem for the role of planktonic cells in biofilm formation and development, Z. Angew. Math. Phys., 72 (2021), 1–17. https://doi.org/10.1007/s00033-021-01561-3 doi: 10.1007/s00033-021-01561-3
    [32] Y. Rohanizadegan, S. Sonner, H. J. Eberl, Discrete attachment to a cellulolytic biofilm modeled by an itô stochastic differential equation, Math. Biosci. Eng., 17 (2020), 2236–2271. https://doi.org/10.3934/mbe.2020119 doi: 10.3934/mbe.2020119
    [33] F. Russo, A. Tenore, M. R. Mattei, L. Frunzo, Multiscale modelling of the start-up process of anammox-based granular reactors, Math. Biosci. Eng., 19 (2022), 10374–10406. https://doi.org/10.3934/mbe.2022486 doi: 10.3934/mbe.2022486
    [34] O. Wanner, W. Gujer, A multispecies biofilm model, Biotechnol. Bioeng., 28 (1986), 314–328. https://doi.org/10.1002/bit.260280304 doi: 10.1002/bit.260280304
    [35] B. D'Acunto, L. Frunzo, M. Mattei, On a free boundary problem for biosorption in biofilms, Nonlinear Anal. Real World Appl., 39 (2018), 120–141. https://doi.org/10.1016/j.nonrwa.2017.06.010 doi: 10.1016/j.nonrwa.2017.06.010
    [36] B. D'Acunto, L. Frunzo, I. Klapper, M. Mattei, Modeling multispecies biofilms including new bacterial species invasion, Math. Biosci., 259 (2015), 20–26. https://doi.org/10.1016/j.mbs.2014.10.009 doi: 10.1016/j.mbs.2014.10.009
    [37] J. M. Hughes, H. J. Eberl, S. Sonner, A mathematical model of discrete attachment to a cellulolytic biofilm using random des, Math. Biosci. Eng., 19 (2022), 6582–6619, https://doi.org/10.3934/mbe.2022310 doi: 10.3934/mbe.2022310
    [38] C. S. Laspidou, B. E. Rittmann, Non-steady state modeling of extracellular polymeric substances, soluble microbial products, and active and inert biomass, Water Res., 36 (2002), 1983–1992. https://doi.org/10.1016/S0043-1354(01)00414-6 doi: 10.1016/S0043-1354(01)00414-6
    [39] F. Abbas, R. Sudarsan, H. J. Eberl, Longtime behavior of one-dimensional biofilm models with shear dependent detachment rates, Math. Biosci. Eng., 9 (2012), 215–239. https://doi.org/10.3934/mbe.2012.9.215 doi: 10.3934/mbe.2012.9.215
    [40] E. Morgenroth, P. A. Wilderer, Controlled biomass removal—the key parameter to achieve enhanced biological phosphorus removal in biofilm systems, Water Sci. Technol., 39 (1999), 33–40. https://doi.org/10.1016/S0273-1223(99)00147-X doi: 10.1016/S0273-1223(99)00147-X
    [41] D. Dubber, N. F. Gray, Replacement of chemical oxygen demand (cod) with total organic carbon (toc) for monitoring wastewater treatment performance to minimize disposal of toxic analytical waste, J. Environ. Sci. Health A, 45 (2010), 1595–1600. https://doi.org/10.1080/10934529.2010.506116 doi: 10.1080/10934529.2010.506116
    [42] I. Douterelo, J. B. Boxall, P. Deines, R. Sekar, K. E. Fish, C. A. Biggs, Methodological approaches for studying the microbial ecology of drinking water distribution systems, Water Res., 65 (2014), 134–156. https://doi.org/10.1016/j.watres.2014.07.008 doi: 10.1016/j.watres.2014.07.008
    [43] M. E. Sieracki, T. L. Cucci, J. Nicinski, Flow cytometric analysis of 5-cyano-2, 3-ditolyl tetrazolium chloride activity of marine bacterioplankton in dilution cultures, Appl. Environ. Microbiol., 65 (1999), 2409–2417. https://doi.org/10.1128/AEM.65.6.2409-2417.1999 doi: 10.1128/AEM.65.6.2409-2417.1999
    [44] B. Merkey, B. Rittmann, D. Chopp, Modeling how soluble microbial products (SMP) support heterotrophic bacteria in autotroph-based biofilms, J. Theor. Biol., 259 (2009), 670–683. https://doi.org/10.1016/j.jtbi.2009.05.010 doi: 10.1016/j.jtbi.2009.05.010
    [45] W. Guo, H. H. Ngo, J. Li, A mini-review on membrane fouling, Bioresour. Technol., 122 (2012), 27–34. https://doi.org/10.1016/j.biortech.2012.04.089 doi: 10.1016/j.biortech.2012.04.089
    [46] J. Mansouri, S. Harrisson, V. Chen, Strategies for controlling biofouling in membrane filtration systems: challenges and opportunities, J. Mater. Chem., 20 (2010), 4567–4586. https://doi.org/10.1039/B926440J doi: 10.1039/B926440J
    [47] N. Cogan, S. Chellam, A method for determining the optimal back-washing frequency and duration for dead-end microfiltration, J. Membr. Sci., 469 (2014), 410–417. https://doi.org/10.1016/j.memsci.2014.06.052 doi: 10.1016/j.memsci.2014.06.052
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